An advanced grid system design was developed to capture accurately the effects of geometrically complex features such as geological features (faults, pinch outs and inclined beddings) and well-related phenomenon (multilateral wells of general orientation) in triangular coordinates. Modeling these effects can have significant impact on the accuracy of the simulation and prediction of reservoir performance as well as reservoir fluid flow using conventional grid designs. The finite difference method provides additional difficulty in capturing geological features in typical reservoir flow and grid model simulators. Hence, the orthogonal collocation method was used for simulating multiphase reservoir flow equations in triangular curvilinear coordinates \(\left[ {\xi \left( r \right),\xi \left( \theta \right),\xi \left( z \right)} \right]\) of domain [0,1] that were derived from Cartesian coordinates \(\left( {x,y,z} \right)\). This was to accommodate general three-dimensional deviated wells and complex reservoir geometry for multiphase flow of hydrocarbon in complex reservoir formations. Based on preliminary field data obtained from multinational oil and gas operator in Nigeria, the proposed model was used to predict saturation, production and petroleum productivity with time and distance in a MATLAB environment. The simulated plots revealed that pressure is parabolic at the center of the reservoir with coordinates \(\xi (r) =0.4257\), reflecting the impact of geological features in the pressure and production flow performance.

中文翻译：

---

基于正交配置方案的复杂水库多相流网格设计与数值模拟

开发了一种先进的网格系统设计，以在三角坐标中准确捕获几何形状复杂的特征（例如地质特征（断层，缩孔和倾斜的地层）和与井相关的现象（多方向的多方向井））的影响。对这些影响进行建模可能会对使用常规网格设计进行油藏动态模拟和预测以及油藏流体流动的准确性产生重大影响。有限差分方法在捕获典型油藏流和网格模型模拟器中的地质特征方面增加了额外的难度。因此，在三角形曲线坐标系中，采用正交配置法模拟了多相油藏流动方程。\（\ left [{\ xi \ left（r \ right），\ xi \ left（\ theta \ right），\ xi \ left（z \ right）} \ right] \）的域[0,1]从笛卡尔坐标\（\ left（{x，y，z} \ right）\）派生。这是为了适应一般的三维偏斜井和复杂的储层几何结构，以适应复杂储层中油气的多相流动。基于从尼日利亚的一家跨国石油和天然气运营商处获得的初步现场数据，该模型被用于预测在MATLAB环境中随时间和距离的饱和度，产量和石油生产率。模拟图表明，压力在储层中心呈抛物线形，坐标为\（\ xi（r）= 0.4257 \），反映了地质特征对压力和生产流程性能的影响。